The present invention is directed, in general, to Coriolis mass flow meters and, in particular, to Coriolis flow meters that take into account the compressibility of the fluids they measure.
Coriolis flow meters were developed for practical industrial use in the late 1970""s by companies such as Micro Motion of Longmont, CO. and others. Generally, a Coriolis mass flow meter is a device that measures mass flowrate of fluids passing through one or more flowtubes, or over surfaces that are intentionally vibrated to cause requisite Coriolis accelerations in the fluid. Some meters operate with parallel flowtubes in a bending mode of vibration, such as the D-series or Elite-series mass flow meters manufactured by Micro-Motion. Other meters operate with a single flowtube in a radial mode of vibration, such as the RMSA series meters manufactured by the assignee of the present invention.
The driven vibration of the flowtubes cause the mass flow stream inside the flowtubes to experience rotational velocity (xcexa9) about an axis perpendicular to the fluid flow direction. This rotational velocity coupled with the velocity of the mass flow rate cause Coriolis accelerations according to the well known and generalized relationship of Equation 1:
Ac=2(xcexa9xc3x97V)xe2x80x83xe2x80x83Equation 1
where:
Ac=the Coriolis acceleration;
xcexa9=the rotational velocity of the fluid; and
V=the linear velocity of the fluid.
Since force is mass multiplied by acceleration, Coriolis Force induced can be determined by adding the mass of the fluid to Equation 1. This is shown in Equation 2:
Fc=xe2x88x922 M*(xcexa9xc3x97V)xe2x80x83xe2x80x83Equation 2
where:
Fc=the Coriolis force; and
M=the mass of the fluid.
The resulting Coriolis forces bear on the flowtube walls, causing the driven vibration pattern to be altered in amplitude, phase or both amplitude and phase, and in proportion to the mass flowrate. This is the fundamental relationship that is exploited in all Coriolis mass flowmeters.
Coriolis mass flow meters have enjoyed tremendous commercial success over the years, because most of them do not intrude into the stream of fluid, are accurate and measure true mass flowrate, at least in theory. Unfortunately, when Coriolis mass flow meters are called upon to measure the mass flow rate of compressible fluids, including most gasses (air, nitrogen, methane, ethylene, etc.) and vapors, the frequency response of the gasses or vapors greatly affects their accuracy. Even when measuring the same fluid, the errors incurred may change as a function of changes in the meters operating frequency or fluid parameters, such as pressure, temperature, density and specific heat. These errors may compound to an overall error of more than 10%, and can be highly dependent upon the design of the flowmeter and the characteristics of the fluid being measured. To complicate matters, while higher frequencies are desirable in terms of signal processing, meter response time and ambient vibration rejection, higher frequency flowtube vibrations tend to exacerbate this problem.
Therefore, what is needed in the art is a way to compensate for these compressibility effects, thereby allowing the inherent benefits of Coriolis mass flow measurement to be employed more effectively with respect to compressible fluids, and to allow Coriolis mass flowmeters to be effectively operated at higher frequencies.
To address the above-discussed deficiencies of the prior art, the present invention provides a Coriolis mass flowmeter having a flowtube and excitation circuitry, coupled to the flowtube, that can excite the flowtube at varying frequencies of vibration and a method of operating the same to compensate for effects of fluid compressibility. In one embodiment, the Coriolis mass flowmeter includes: (1) flowrate measurement circuitry, coupled to the flowtube, that measures a first mass flowrate of a fluid flowing through the flowtube at a first vibration frequency and a second mass flowrate of the fluid at a second vibration frequency and (2) fluid compressibility compensation circuitry, coupled to the flowrate measurement circuitry, that employs the first and second mass flowrates to determine a frequency response of the fluid and a fluid compressibility compensation adjustment from the frequency response.
Implicit in the relationship set forth in the Background of the Invention set forth above is the assumption that the rotational velocity term (xcexa9) in equations (1) and (2), above, as delivered to the fluid by the flowtube wall, is felt simultaneously by the entire fluid stream and thereby causes a simultaneous and directly proportionate force (Fc) of the fluid back onto the wall. Here is the problem as it relates to compressible fluids.
A compressible fluid is itself a mass-spring-damper (MSD) system in which mass is represented by the fluid""s density, stiffness is represented by the fluid""s bulk modules of elasticity and damping is represented by the fluid""s viscosity. (Bulk modulus of elasticity, k, is inverse to adiabatic compressibility, xcex20=1/xcex3p.) For purposes of the present invention, however, xe2x80x9ccompressibilityxe2x80x9d is employed in a general sense to mean that a fluid in a contained volume can be compressed to a new volume by the application of work on the system, (i.e., forcing a piston to compress gas in a cylinder). All fluids are compressible to some degree; gasses tend to be more compressible than liquids.
As with any MSD system, the response of the system depends on values of the parameters involved (i.e., mass, spring constant, damping), along with boundary conditions. In the case of compressible fluid inside the flowtube of a Coriolis mass flowmeter, the fluid is accelerated perpendicular to the axis of the flowtube (across the flowtube diameter). Therefore, the important boundary conditions for this purpose are the dimensions and shape of the inside of the flowtube which, in combination with the fluid parameters, cause the existence of natural transverse resonances of the fluid vibrating within the confines of the flowtube. These natural transverse resonances give rise, in turn, to frequency response characteristics (evidenced in curves) relating the response of the fluid (pressure against the flowtube wall) to various frequency excitations.
Heretofore, Coriolis flowmeter signal processing has assumed that the fluid is incompressible and therefore that the fluid reacts instantly to the imposed accelerations from the flowtube wall. However, it can now be seen that compressible fluids will react according to their frequency response characteristics, as will be described in greater detail. If the frequency response characteristics were fixed, an initial calibration would compensate for errors. However, the shape of the frequency response curves may change as a function of changes in the flowtube and fluid parameters, such as fluid density, temperature, pressure, viscosity, molecular weight, etc. In addition, the excitation frequency of the flowmeter, which sets the operating point on the frequency response curve, is also subject to variations caused by fluid pressure, temperature, density, viscosity, pipeline stress, and others. Therefore, the resulting response of the device to mass flowrate is unpredictable unless the operating point on the operating frequency response curve is known. The present invention therefore describes several systems and methods of determining the shape of the frequency response curve, the operating point on the frequency response curve, or both, during operation of the meter and regardless of changing fluid and flowtube parameters.
Certain embodiments of the present invention take advantage of the observation that even though the frequency response curves appear complicated, having multitudes of natural resonances all contributing to the fluid""s total response, the equation of the curve may be accurately reduced to one or two variables, which may easily be determined or assumed as hereinafter described. Since all the contributing natural resonances of the fluid are subject to the same boundary condition (the inside diameter or shape of the flowtube), the resulting resonance values bear a proportionate relationship to each other, even as gas parameters change. In these certain embodiments, the entire equation to be reduced (in its simplest form) to one variable. In one embodiment, knowing the basic form of the equation in terms of one variable allows the entire response curve to be approximated by obtaining only one additional piece of information.
In an embodiment to be illustrated and described, the additional piece of information is acquired by making a second flow measurement at a different frequency than the one at which the first measurement was taken. Since the response of the gas varies at different frequencies according to its response curve, a different flow measurement reading is attained at a different frequency. The variation between the flow measurements is functionally related to the frequency response of the gas. Therefore, by evaluating flow measurements taken at one operating frequency versus another, the frequency response characteristic of the gas can be determined, and the correct mass flowrate can be calculated, regardless of the fluid and its current characteristics.
In an alternative embodiment to be illustrated and described, the frequency response curve is determined by calculation based on fluid properties and the configuration of the flow meter. Once determined, the response value can be determined for the operating frequency of the flow meter, and the appropriate compensation applied.
In yet another embodiment, the frequency response curve is determined by finding one or more resonance points along its curve. Again, since the value of these resonance points bear a fixed relationship with each other, at a minimum, only one resonance point needs to be found to determine the entire curve with an acceptably high degree of accuracy. The curve, along with the frequency of the operating point or points of the flow meter, can then be employed to compensate for any changes in the frequency response characteristics of the fluid. In another embodiment, the frequency response of the fluid is determined directly by exciting the fluid and measuring its response through a frequency range or at specified points. This may be done with conventional magnet/coil transducers, piezoelectric transducers, or other conventional transducers or actuators.
The foregoing has outlined, rather broadly, preferred and alternative features of the present invention so that those skilled in the art may better understand the detailed description of the invention that follows. Additional features of the invention will be described hereinafter that form the subject of the claims of the invention. Those skilled in the art should appreciate that they can readily use the disclosed conception and specific embodiment as a basis for designing or modifying other structures for carrying out the same purposes of the present invention. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the invention in its broadest form.